Research On The Effect Of The Toxin-producing Plankton On Marine Ecosystem

Mathematical biology is a new subject of the interaction of biology and mathematics, it mainly solves some practical problems in the nature by some mathematical tools and techniques. In this paper, we investigate the dynamic behavior of toxin producing phytoplankton and zooplankton, and introduce the nature and reason of the bloom. We also discuss the effect of bloom on the ecology system.In the second chapter, we build up a predator-prey model, containing of the toxin producing phytoplankton. In the third chapter, we build up an infectious disease model, containing of two toxin producing phytoplanktons.We analysis the stability of these models, and we also discuss the stability of these models with toxin. As a result, we find that, because of the effect of toxin of phytoplankton, the number of every species decreases when the system reach a equilibrium state. What is more, the density value of each species in the equilibrium state with which system contains of three species are lower than the density value of themselves in the equilibrium state with which system contains of only any two species.In the predator-prey mode, by the numerical modeling, we find that when the toxin producing phytoplankton affect the two predators, the scope and probability of coexistence increases. In the infectious disease model, by the numerical modeling, we find that when the infected phytoplankton and the susceptible phytoplankton both can produce toxins, the probability of coexistence increases in the whole level, and the density value of every species decreases. As a result, the ecosystem is easier to reach equilibrium state. The release of toxin substance by phytoplankton may weaken or terminate the planktoniic bloom.